Abstract
We present a multi-conclusion natural deduction calculus characterizing the dynamic reasoning typical of Adaptive Logics. The resulting system AdaptiveND is sound and complete with respect to the propositional fragment of adaptive logics based on CLuN. This appears to be the first tree-format presentation of the standard linear dynamic proof system typical of Adaptive Logics. It offers the advantage of full transparency in the formulation of locally derivable rules, a connection between restricted inference-rules and their adaptive counterpart, and the formulation of abnormalities as a subtype of well-formed formulas. These features of the proposed calculus allow us to clarify the relation between defeasible and multiple-conclusion approaches to classical recapture.
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Notes
- 1.
See also footnote 10 of Batens (2008) for a discussion of this distinction.
- 2.
‘A is finally derived from \(\Gamma \) on line i of a proof at stage s iff (i) A is the second element of line i, (ii) line i is not marked at stage s, and (iii) every extension of the proof in which line i is marked may be further extended in such a way that line i is unmarked.’ [Batens 2007, 229].
- 3.
See Allo (2016, 18ff) for a more detailed reconstruction of this debate.
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Acknowledgements
Patrick Allo—Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 657017.
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Allo, P., Primiero, G. (2019). Annotated Natural Deduction for Adaptive Reasoning. In: Başkent, C., Ferguson, T. (eds) Graham Priest on Dialetheism and Paraconsistency. Outstanding Contributions to Logic, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-25365-3_19
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